01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 | /** 2D HEAT EQUATION SOLVER** Copyright (c) 2008 Tony Saad <saadtony@gmail.com>* (Written by Tony Saad <saadtony@gmail.com>)** This program is free software; you can redistribute it and/or modify* it under the terms of the GNU General Public License as published by* the Free Software Foundation; either version 2 of the License, or* (at your option) any later version.** This program is distributed in the hope that it will be useful,* but WITHOUT ANY WARRANTY; without even the implied warranty of* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the* GNU General Public License for more details.** You should have received a copy of the GNU General Public License* along with this program; if not, write to the Free Software* Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA*//*--------------------------------------------------------*//* INCLUDE HEADERS/*--------------------------------------------------------*/#include <stdio.h>#include <stdlib.h>#include <math.h>#include <ctime>/*--------------------------------------------------------*//* STRUCTURES/*--------------------------------------------------------*/struct ProblemInfo { int numberOfNodesX; int numberOfNodesY; double endSimulationTime; double thermalDiffusivity; double CFL;};/*--------------------------------------------------------*//* FUNCTION PROTOTYPES/*--------------------------------------------------------*/bool processUserInput(ProblemInfo &theProblemInfo);void setupBoundaryConditions(double** theArray, int arraySizeX, int arraySizeY);void initializeInteriorNodes(double** theArray, int arraySizeX, int arraySizeY);void initializeArray(double** theArray, int arraySizeX, int arraySizeY);int* makeIntArray(int arraySize);int** make2DIntArray(int arraySizeX, int arraySizeY);double* makeDoubleArray(int arraySize);double** make2DDoubleArray(int arraySizeX, int arraySizeY);void saveToFile(ProblemInfo theProblemInfo, double** theData,char* theFileName);/*--------------------------------------------------------*//* MAIN PROGRAM/*--------------------------------------------------------*/int main(int argc, char* argv[]) { /***********************************************************/ /* VARIABLES /***********************************************************/ int nNodesX, nNodesY; int ix = 0, jy =0; double endSimulationTime = 1.0, CFL = 0.25, deltaT, deltaX, deltaY, deltaXSquared, deltaYSquared; clock_t startCPUTime = 0, endCPUTime = 0, totalCPUTime = 0; ProblemInfo probInfo; /* process user input */ if (!processUserInput(probInfo)) return 0; startCPUTime = clock(); nNodesX = probInfo.numberOfNodesX; nNodesY = probInfo.numberOfNodesY; deltaX =(double) 1.0/probInfo.numberOfNodesX; deltaY =(double) 1.0/probInfo.numberOfNodesY; deltaXSquared = deltaX*deltaX; deltaYSquared = deltaY*deltaY; CFL = probInfo.CFL; deltaT = CFL*(deltaXSquared*deltaYSquared)/((deltaXSquared+deltaYSquared)*probInfo.thermalDiffusivity); /* memory allocation */ double** uOld = make2DDoubleArray(nNodesX,nNodesY); initializeArray(uOld,nNodesX,nNodesY); double** uNew = make2DDoubleArray(nNodesX,nNodesY); setupBoundaryConditions(uNew,nNodesX,nNodesY); /***********************************************************/ /* COMPUTATION /***********************************************************/ int iter = 0; while(iter++*deltaT <= probInfo.endSimulationTime) { if (iter % 100 == 0) { printf("Iteration: %i - Current Time = %lf s\n", iter-1, (iter-1)*deltaT); } /* calculate the new values of the dependant variable */ for (ix = 1; ix < (nNodesX-1); ix++) { for (jy = 1; jy < (nNodesY-1) ;jy++){ uNew[ix][jy] = uOld[ix][jy] + CFL*(uOld[ix+1][jy] + uOld[ix-1][jy] - 4*uOld[ix][jy] + uOld[ix][jy-1] + uOld[ix][jy+1]); } } /* set uOld = uNew */ for (ix = 1; ix < (nNodesX-1); ix++) { for (jy = 1; jy < (nNodesY-1) ;jy++){ uOld[ix][jy] = uNew[ix][jy]; } } } endCPUTime = clock(); /* compute the total wall time */ totalCPUTime= endCPUTime-startCPUTime; /* compute the maximum wall time */ printf("Wall clock time %lf s\n",(double) totalCPUTime/CLOCKS_PER_SEC); saveToFile(probInfo,uNew,"C:\\2D Heat Equation.dat"); /* works only in Windows */ system("pause"); return 0;}/*--------------------------------------------------------*//* FUNCTIONS/*--------------------------------------------------------*/bool processUserInput(ProblemInfo &theProblemInfo) { printf("Enter the number of nodes in the x direction:"); fflush(stdout); scanf("%d",&theProblemInfo.numberOfNodesX); printf("Enter the number of nodes in the y direction:"); fflush(stdout); scanf("%d",&theProblemInfo.numberOfNodesY); if (theProblemInfo.numberOfNodesX == 0 || theProblemInfo.numberOfNodesY==0) return 0; printf("Enter thermalDiffusivity:"); fflush(stdout); scanf("%lf",&theProblemInfo.thermalDiffusivity); printf("Enter end simulation time:"); fflush(stdout); scanf("%lf",&theProblemInfo.endSimulationTime); printf("Enter the Courant-Friedrichs-Lewy (CFL) number \n (For stability, the CFL number should be less than 0.25 \n based on a different number of nodes in the X and Y directions):"); fflush(stdout); scanf("%lf",&theProblemInfo.CFL); return 1;}void setupBoundaryConditions(double** theArray,int arraySizeX, int arraySizeY) { /* set boundary conditions for ix, jy = 0 and ix, jy = n-1 */ /* Here, we are using Dirichlet conditions */ int ix, jy; double leftBC = 10, rightBC = 10, topBC = 20, bottomBC = 20; /* setup the bottom and top BCs, jy = 0 and jy = n-1 or arraySizeY - 1 */ for (ix = 0; ix < arraySizeX; ix++) { theArray[ix][0] = bottomBC; //bottom BC theArray[ix][arraySizeY-1] = topBC; //top BC } /* setup the left and right BCs, ix = 0 and ix = arraySizeX - 1 */ for (jy = 0; jy < arraySizeY; jy++) { theArray[0][jy] = leftBC; //left BC theArray[arraySizeX-1][jy] = rightBC; //right BC } /* set the values at the corner nodes as averages of both sides*/ // bottom left theArray[0][0] = (leftBC + bottomBC)*0.5; // top left theArray[0][arraySizeY-1] = 0.5*(topBC + leftBC); // top right theArray[arraySizeX-1][arraySizeY-1] = 0.5*(topBC + rightBC); // bottom right theArray[arraySizeX-1][0] = 0.5*(bottomBC + rightBC);}void initializeInteriorNodes(double** theArray, int arraySizeX, int arraySizeY) { int ix, jy; for (ix = 1; ix <= arraySizeX - 2; ix++) { for (jy = 1; jy <= arraySizeY - 2; jy++) { theArray[ix][jy] = 0.0; } }}void initializeArray(double** theArray, int arraySizeX, int arraySizeY) { setupBoundaryConditions(theArray,arraySizeX,arraySizeY); initializeInteriorNodes(theArray,arraySizeX,arraySizeY);}double** make2DDoubleArray(int arraySizeX, int arraySizeY) { double** theArray; theArray = (double**) malloc(arraySizeX*sizeof(double*)); for (int ix = 0; ix < arraySizeX; ix++) { theArray[ix] =(double*) malloc(arraySizeY*sizeof(double)); } return theArray;}double* makeDoubleArray(int arraySize) { double* theArray; theArray = (double*) malloc(arraySize*sizeof(double)); return theArray;}int* makeIntArray(int arraySize) { int* theArray; theArray = (int*) malloc(arraySize*sizeof(int)); return theArray;}int** make2DIntArray(int arraySizeX, int arraySizeY) { int** theArray; theArray = (int**) malloc(arraySizeX*sizeof(int*)); for (int ix = 0; ix < arraySizeX; ix++) { theArray[ix] =(int*) malloc(arraySizeY*sizeof(int)); } return theArray;}void saveToFile(ProblemInfo theProblemInfo, double** theData, char* theFileName) { int nNodesX = theProblemInfo.numberOfNodesX; int nNodesY = theProblemInfo.numberOfNodesY; double deltaX =(double) 1.0/theProblemInfo.numberOfNodesX; double deltaY =(double) 1.0/theProblemInfo.numberOfNodesY; FILE* theDataFile; theDataFile = fopen(theFileName,"w"); for (int ix = 0; ix < nNodesX; ix++) { for (int jy = 0; jy < nNodesY ;jy++){ fprintf(theDataFile,"%lf %lf %lf\n",ix*deltaX,jy*deltaY,theData[ix][jy]); } fprintf(theDataFile,"\n"); } fclose(theDataFile);} |
